# Mathematical Sciences Research Institute

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# Seminar

Asymptotics for the coefficients of Kac-Wakimoto characters March 28, 2011 (01:00 PM PDT - 01:50 PM PDT)
Parent Program: -- MSRI: Simons Auditorium
Speaker(s) Karl Mahlburg
Description Location: Simons Auditorium

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Asymptotics for the coefficients of Kac-Wakimoto characters
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I will discuss recent work on asymptotic series expansions for the coefficients of character formulas of affine Lie superalgebras studied by Kac and Wakimoto.  Such character formulas encode the graded dimensions of root spaces in a generating function, and the modularity of such functions famously arose in Conway and Norton's "Monstrous moonshine" conjectures, as well as Kac's Denominator formula.

In the situation discussed here, the character formula is the product of a modular form and a "mock" modular form (a class of real-analytic automorphic forms whose theory has only recently been developed).  The Hardy-Ramanujan Circle Method is used to determine the coefficients, which requires new results on precise modular transformation formulas for higher-level mock modular forms.

Video